More information at http://hosted.msri.org/alg/ 3:45 PM Quantitative Cocycles Speaker: Persi Diaconis Abstract: Choosing sections for natural maps is a basic mathematical activity. In joint work with Soundarajan and Shao we study the problem of choosing "nice" sections. Here is a typical theorem: Let $G$ be a finite group, $H$ a normal subgroup. Let $X$ be coset representatives for $H$ in $G$. suppose the proportion of $x,y$ in $X$ with $xy \in X$ is more than $1-1/60$. Then the extension splits. There are many variations, many open problems and applications to basic arithmetic and computer science. 5:00 PM Clifford Algebras and the Ranks of Modules in Free Resolutions Speaker: David Eisenbud Abstract: A conjecture of Horrocks, and independently of Buchsbaum and myself, asserts that the sum of the ranks of the modules in the free resolution of a module annihilated by a regular sequence of length c is at least $2^{c}$. I'll describe a related new conjecture by Irena Peeva and myself and show how we proved a special case, in our work on complete intersections, using results on Clfford algebras and enveloping algebras.